An infinite product formula for Uq(sl(2)) dynamical coboundary element

An infinite product formula for U q (sl(2)) dynamical coboundary element. Abstract We give a short summary of results and conjectures in the theory of dynamical quantum group related to the dynamical coboundary equation also known as IRF-Vertex transform. O.Babelon has shown that the dynamical twist F (x) of Uq(sl(2)) is a dynamical coboundary M (x) i.e F (x)M1(xq h 2)M2(x) = ∆(M (x)). We give a new formula for this element M (x) as an infinite product and give a new proof of the coboundary relation. Our proof involves the quantum Weyl group element, giving possible hint for the generalization to higher rank case.